Optimization Models for Turbine Location in Wind Farms

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Abstract

The topic of this thesis is wind farm optimization. The goal is to be able to decide where to install wind turbines within a given region in order to maximize the power output in two different scenarios: For a fixed number of turbines with free placement, and for a limited number of possible locations and a variable number of turbines with a fixed cost associated with the installation of each turbine that is subtracted from the power output. These are referred to as "Problem 1" and "Problem 2". First, we develop a new, simple wake model. It is based on a model that was described by Katic et. al. in 1986, and then we make some improvements based on the authors' own comments and data. This is then further developed into complete mathematical models for Problem 1 and Problem 2. We consider a few heuristic methods for carrying out the optimization, including one that we have not seen in the literature. These are tried out on simple test cases. Finally, we try out exact optimization on two simple cases, and try out the heuristic methods on a larger sample of cases. We conclude that the new wake model, combined with the method that displays the best performance in the experiments, appears to be a useful tool in designing wind farms.